To gain a better understanding of the advection of reaction fronts in a porous medium, we consider the similarities and the differences between the advection of wavefronts in a packed bed and in a flat gap or a pipe. The model calculations are based on the reaction -diffusion-advection equation for cubic autocatalysis, with the flow field in a gap taken into account explicitly. The analysis performed allows us to conclude that, in the "wide gap" limit, i.e., when the ratio of the gap (or pore) width to the front width is large, for the adverse flow in a porous medium one can expect the formation of stationary wavefronts for a wide range of flow velocities, if one takes into account that advection in a porous medium can effectively quench the axial diffusion of an autocatalyst. These predictions are verified experimentally for a non-oscillatory autocatalytic reaction, viz., the oxidation of thiosulfate with chlorite, carried out in a packed bed of glass beads. It is demonstrated for the first time that, in the case of an adverse flow, the stationary wavefronts in the "wide gap" limit are indeed observed for this reaction, and this limit can be achieved by, e.g., increasing the concentrations of the key reactants. We suggest that the observations of stationary wavefronts in the oscillatory Belousov-Zhabotinsky reaction reported earlier can be accounted for in similar terms. The formation of stationary wavefronts in a packed bed is favored owing to the much larger flow dispersion effects (the ratio of the largest flow velocity to the average flow velocity) in a porous medium as compared to flow in a gap or a pipe. Nevertheless, for a correct description of the effects of advection on the wavefront propagation, it is not appropriate to substitute the dispersion coefficient for diffusivity in the reaction -diffusion- advection equation.